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I have a $100\times 100$ matrix with entries $a_{ij}=(-1)^{i+j}$. Are the columns of $A$ a linearly independent subset of $\mathbb{R}^{100}$?

I can see diagonal entries are all $1$, and other are $1,-1$, please help how to proceed

  • 1
    Does the first column look like the third column? How similar are they? The phrase "checkerboard pattern" comes to mind. – 2017-02-22
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    Aren't there only two distinct columns? – 2017-02-22
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    Obviously NOT. As the matrix is singular. – 2017-02-22

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